34,074 research outputs found
Rewriting Codes for Joint Information Storage in Flash Memories
Memories whose storage cells transit irreversibly between
states have been common since the start of the data storage
technology. In recent years, flash memories have become a very
important family of such memories. A flash memory cell has q
states—state 0.1.....q-1 - and can only transit from a lower
state to a higher state before the expensive erasure operation takes
place. We study rewriting codes that enable the data stored in a
group of cells to be rewritten by only shifting the cells to higher
states. Since the considered state transitions are irreversible, the
number of rewrites is bounded. Our objective is to maximize the
number of times the data can be rewritten. We focus on the joint
storage of data in flash memories, and study two rewriting codes
for two different scenarios. The first code, called floating code, is for
the joint storage of multiple variables, where every rewrite changes
one variable. The second code, called buffer code, is for remembering
the most recent data in a data stream. Many of the codes
presented here are either optimal or asymptotically optimal. We
also present bounds to the performance of general codes. The results
show that rewriting codes can integrate a flash memory’s
rewriting capabilities for different variables to a high degree
Rewriting Flash Memories by Message Passing
This paper constructs WOM codes that combine rewriting and error correction
for mitigating the reliability and the endurance problems in flash memory. We
consider a rewriting model that is of practical interest to flash applications
where only the second write uses WOM codes. Our WOM code construction is based
on binary erasure quantization with LDGM codes, where the rewriting uses
message passing and has potential to share the efficient hardware
implementations with LDPC codes in practice. We show that the coding scheme
achieves the capacity of the rewriting model. Extensive simulations show that
the rewriting performance of our scheme compares favorably with that of polar
WOM code in the rate region where high rewriting success probability is
desired. We further augment our coding schemes with error correction
capability. By drawing a connection to the conjugate code pairs studied in the
context of quantum error correction, we develop a general framework for
constructing error-correction WOM codes. Under this framework, we give an
explicit construction of WOM codes whose codewords are contained in BCH codes.Comment: Submitted to ISIT 201
Time-Space Constrained Codes for Phase-Change Memories
Phase-change memory (PCM) is a promising non-volatile solid-state memory
technology. A PCM cell stores data by using its amorphous and crystalline
states. The cell changes between these two states using high temperature.
However, since the cells are sensitive to high temperature, it is important,
when programming cells, to balance the heat both in time and space.
In this paper, we study the time-space constraint for PCM, which was
originally proposed by Jiang et al. A code is called an
\emph{-constrained code} if for any consecutive
rewrites and for any segment of contiguous cells, the total rewrite
cost of the cells over those rewrites is at most . Here,
the cells are binary and the rewrite cost is defined to be the Hamming distance
between the current and next memory states. First, we show a general upper
bound on the achievable rate of these codes which extends the results of Jiang
et al. Then, we generalize their construction for -constrained codes and show another construction for -constrained codes. Finally, we show that these two
constructions can be used to construct codes for all values of ,
, and
When Do WOM Codes Improve the Erasure Factor in Flash Memories?
Flash memory is a write-once medium in which reprogramming cells requires
first erasing the block that contains them. The lifetime of the flash is a
function of the number of block erasures and can be as small as several
thousands. To reduce the number of block erasures, pages, which are the
smallest write unit, are rewritten out-of-place in the memory. A Write-once
memory (WOM) code is a coding scheme which enables to write multiple times to
the block before an erasure. However, these codes come with significant rate
loss. For example, the rate for writing twice (with the same rate) is at most
0.77.
In this paper, we study WOM codes and their tradeoff between rate loss and
reduction in the number of block erasures, when pages are written uniformly at
random. First, we introduce a new measure, called erasure factor, that reflects
both the number of block erasures and the amount of data that can be written on
each block. A key point in our analysis is that this tradeoff depends upon the
specific implementation of WOM codes in the memory. We consider two systems
that use WOM codes; a conventional scheme that was commonly used, and a new
recent design that preserves the overall storage capacity. While the first
system can improve the erasure factor only when the storage rate is at most
0.6442, we show that the second scheme always improves this figure of merit.Comment: to be presented at ISIT 201
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